Tracking error - Financial theory
- Moneyterms: investment, finance and business explained (2024)
Tracking error is a measurement of how much the return on a portfolio deviates from the return on its benchmark index. It is a very important metric for index trackers.
Tracking error is the standard deviation of the differences between the return on the portfolio and the return on the benchmark; the standard deviation of the excess returns:
σ2 = 1/(n - 1) Σ(xi - yi)2
Where σ is the tracking error n is the number of periods over which it is measured x is the percentage return on the portfolio in period i y is the percentage return on the benchmark
Some sources claim that the average error should be subtracted from right side of the equations above. That would give us the standard deviation of the tracking error from the tracking error over time. The formula given here appears preferable as it is a measure of deviation from the benchmark itself.
In order to make the tracking error comparable it should be annualised. In order to do the right right of the equation should be multiplied by the number of periods in an year. Equivalents σ multiplied by the root of the number of periods in an year. So if the error is based on monthly returns, it should be multiplied by root 12 to annualise.
Tracking error may be calculated from historical data (as above) or estimated for future returns. The former is called ex-post tracking error, and the latter ex-ante (standard terminology for statistics).
The causes of tracking error
For an actively managed fund tracking error is a measure of how actively managed it is. A closet tracker will have a low tracking error, a very actively managed fund a high tracking error.
An index tracker has two different causes of tracking error:
the differences in the composition of the portfolio and the benchmark.
The second of these is a direct result of the need to minimise the first. The simplest way to construct a tracker would be to simply hold every security in an index in proportion to its weighting in the index. The problem with this is that it increases trading costs as it involves holding a large number of securities.
In order to control trading costs, tracker funds hold a selection of securities that is statistically likely to replicate the performance of the index. This requires statistical analysis to construct the portfolio that will most accurately track the index at the lowest cost. This is why tracker funds are run by quants.
A portfolio that is a selected sample of the index will clearly not perform exactly as the index does. It should, however, perform very closely in like with the index.
In addition to the costs of actually trading the portfolio, the fees charged by fund managers also reduce the performance. While these are much lower than the fees charged by active fund managers, they still have a significant effect over time.
Tracking error is the standard deviation of the difference between the returns of an investment and its benchmark. Given a sequence of returns for an investment or portfolio and its benchmark, tracking error is calculated as follows: Tracking Error = Standard Deviation of (P - B)
What is Tracking Error? Tracking error is a measure of financial performance that determines the difference between the return fluctuations of an investment portfolio and the return fluctuations of a chosen benchmark. The return fluctuations are primarily measured by standard deviations.
It is defined as the standard deviation of the excess return, that is, the difference between the return on a portfolio and the return on its benchmark. Unlike VaR, which is usually measured for shorter periods, tracking error is typically meas- ured in terms of monthly returns.
Tracking error is simply the difference between the scheme's return and that of the benchmark. This measures how closely a mutual fund scheme replicates the returns of the identified benchmark. Larger the deviation from its benchmark returns, higher the tracking error a scheme is said to have.
A low tracking risk implies that a portfolio is closely following the benchmark. A high tracking error implies that a portfolio is volatile relative to the benchmark and that returns are drifting from the benchmark. Investors prefer a low tracking error.
Here are some of the other factors that influence tracking error: Portfolio size. Variations in market capitalization, investment approach, timing, and other portfolio features. Alterations in index constituents.
Standard Deviation tells you the absolute amount up and down, whereas Tracking Error tells you how different the fund is from the index. If the index is up 20% and a fund is up 30%, that's pretty different, as opposed to another fund maybe that's up 21% that would have a lower Tracking Error.
Tracking error is the standard deviation of the difference between the returns of an investment and its benchmark. Given a sequence of returns for an investment or portfolio and its benchmark, tracking error is calculated as follows: Tracking Error = Standard Deviation of (P - B)
Several factors affect the level of tracking error. The major factors include: Number of stocks in the portfolio. Portfolio market capitalization and style difference relative to the benchmark.
VaR is often criticized for offering a false sense of security, as VaR does not report the maximum potential loss. One of its limitations is that the statistically most likely outcome isn't always the actual outcome.
In finance, tracking error or active risk is a measure of the risk in an investment portfolio that is due to active management decisions made by the portfolio manager; it indicates how closely a portfolio follows the index to which it is benchmarked.
Tracking error is the annualized standard deviation of daily return differences between the total return performance of the fund and the total return performance of its underlying index. In laymen's terms, tracking error basically looks at the volatility in the difference of performance between the fund and its index.
Limited Scope: Tracking error only measures the deviation of a portfolio's return from its benchmark. It does not provide any information about the quality of the portfolio's investments. For example, a portfolio with a low tracking error may still have poor investment choices that result in low returns.
Among large cap funds, Navi Nifty 50 Index Fund has the lowest tracking error of 0.01% among large cap index funds followed by Navi Nifty Next 50 Index Fund with tracking error of 0.02%. In the midcap space, Navi Nifty Midcap 150 Index Fund has the lowest tracking error of 0.01%.
In an ideal case scenario, an index fund must have a tracking error of zero when comparing performance to its benchmark. But in reality, index funds lean towards the 1%, -2% range.
Fund management and trading fees are often cited as the largest contributor to tracking error. It is easy to see that even if a given fund tracks the index perfectly, it will still underperform that index by the amount of the fees that are deducted from a fund's returns.
Tracking error is the volatility of the difference in returns between the portfolio and the benchmark.Beta can be calculated as correl(portfolio, bmk) * ( vol portfolio / vol bmk).
Active Share and Tracking Error are two metrics that measure different aspects of a portfolio's performance. Active Share measures the degree of active management in a portfolio, while Tracking Error measures the deviation of a portfolio's returns from its benchmark.
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